1. 樑與鋼架結構分析 Analysis of Beams and Frames
Chapter 11
樑與鋼架結構分析
Analysis of Beams and Frames

2. Contents 11.1 BEAM3: 2D樑元素 BEAM3: 2D Elastic Beam Element
11.2 實例: 腳踏車架設計
Example: Design of a Bicycle Frame
11.3 實例: 鋼弦的震動分析
Example: Vibration of a String Under Tension
11.4 實例: 升降平台結構分析
Example: Structural Analysis of a Lift Platform
11.5 樑元素瀏覽
Overview of Beam Elements
11.6 練習題
Exercises

3. BEAM3: 2D樑元素 BEAM3: 2D Elastic Beam Element
第11.1節
BEAM3: 2D樑元素
BEAM3: 2D Elastic Beam Element

4. BEAM3元素描述

5. 11.1.2 BEAM3輸入資料 Element Name BEAM3 Nodes I, J Degrees of Freedom
UX, UY, ROTZ
Real Constants
AREA, IZZ, HEIGHT, SHEARZ, ISTRN, ADDMAS
Material Properties
EX, NUXY, GXY, ALPX, DENS, DAMP
Surface Loads
Pressure face 1, face 2, face 3, face 4
Body Loads
Temperature -- T1, T2, T3, T4
Special Features
Stress stiffening, Large deflection, etc.
etc.

6. BEAM3輸出資料

7. 實例: 腳踏車架設計 Example: Design of a Bicycle Frame
第11.2節
實例: 腳踏車架設計
Example: Design of a Bicycle Frame

8. 問題描述 31 10 18 32 36 12 15

9. ANSYS Procedure (1/3) 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18
FINISH
/CLEAR
/UNITS, BIN
  D       = 1 ! Outer Diameter
  T       = 1/16 ! Thickness
  PI      = 4*ATAN(1)
  PSEAT   = 150*2.5 ! Load on seat
  PHANDLE = 25*2.5 ! Load on handle
/PREP7
  ET, 1, BEAM3
  MP, EX, 1, 30E6
  MP, NUXY, 1, 0.3
  AREA = PI*(D**2-(D-T)**2)/4
  IZZ  = PI*(D**4-(D-T)**4)/64
  R, 1, AREA, IZZ, D

10. ANSYS Procedure (2/3) 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
  K, 1,  0,  0
  K, 2, 18,  0
  K, 3, 36,  0
  K, 4, 10, 15
  K, 5, 31, 15
  K, 6, 32, 12
  L, 1, 2
  L, 4, 5
  L, 1, 4
  L, 2, 4
  L, 2, 6
  L, 5, 6
  L, 6, 3
  ESIZE, 2
  LMESH, ALL
  FINISH 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51
/SOLU
  NLEFT   = NODE(0,0,0) ! Left support
  NRIGHT  = NODE(36,0,0) ! Right support
  NSEAT   = NODE(10,15,0) ! Seat
  NHANDLE = NODE(31,15,0) ! Handle
  D, NLEFT,  UX, 0
  D, NLEFT,  UY, 0
  D, NRIGHT, UY, 0
  F, NSEAT,   FY, -PSEAT
  F, NHANDLE, FY, -PHANDLE
  /PBC, ALL,, ON
  EPLOT
  SOLVE
  FINISH

11. ANSYS Procedure (3/3) 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69
/POST1
  PLDISP, 2
  ETABLE, MFORX, SMISC, 1
  ETABLE, MFORY, SMISC, 2
  ETABLE, MMOMZ, SMISC, 6
  ETABLE, SDIR,  LS,    1
  ETABLE, SBYT,  LS,    2
  ETABLE, SBYB,  LS,    3
  ETABLE, SMAX,  NMISC, 1
  ETABLE, SMIN,  NMISC, 2
  PRETAB, MFORX, MFORY, MMOMZ
  PRETAB, SDIR, SBYT, SBYB, SMAX, SMIN
  PLETAB, SDIR
  PLETAB, SBYT
  PLETAB, SMAX
  PLETAB, SMIN

12. 實例: 鋼弦的震動分析 Example: Vibration of a String Under Tension
第11.3節
實例: 鋼弦的震動分析
Example: Vibration of a String Under Tension

13. 問題描述

14. ANSYS Procedure (1/3) 01 02 03 04 05 06 07 08 09 10 11 12 13
FINISH
/CLEAR
/TITLE, VM53 (lb-in-s)
  D     = 1/16 ! Diameter
  PI    = 4*ATAN(1) ! Constant
  AREA  = PI*D**2/4 ! Cross section
  IZZ   = PI*D**4/64 ! Moment of inertia
  ISTRN = ! Initial strain
  E     = 30E6 ! Steel
  NU    = 0.3 ! Steel
  RO    = ! Steel
  L     = 100 ! Length of string

15. ANSYS Procedure (2/3) 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
/PREP7
  ET, 1, BEAM3
  R, 1, AREA, IZZ, D,, ISTRN
  MP, EX, 1, E
  MP, NUXY, 1, NU
  MP, DENS, 1, RO
  N,  1, 0, 0
  N, 14, L, 0
  FILL
  E, 1, 2
  EGEN, 13, 1, -1
  FINISH
/SOLU
  D,   1, ALL, 0
  D,  14, ALL, 0
  PSTRES,ON 
  SOLVE 37 38 39 40 41 42 43 44 45 46 47 48 49
/POST1
  ETABLE, STRESS, LS, 1
  PRETAB, STRESS
  FINISH
/SOLU
   
  ANTYPE, MODAL
  MODOPT, SUBSP, 3
  PSTRES, ON
  SOLVE

16. ANSYS Procedure (3/3) 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70
/POST1
  SET, LIST
  /TRIAD, OFF
  /COLOR, PBAK, OFF
  SET, 1, 1
  /WINDOW, 1, -1, 1.67, 0.4, 1.0
  PLDISP, 2
  /NOERASE
  /WINDOW, 1, OFF
  SET, 1, 2
  /WINDOW, 2, -1, 1.67, -0.3, 0.3
  /WINDOW, 2, OFF
  SET, 1, 3
  /WINDOW, 3, -1, 1.67, -1.0, -0.4

17. 實例: 升降平台結構分析 Example: Structural Analysis of a Lift Platform
第11.4節
實例: 升降平台結構分析
Example: Structural Analysis of a Lift Platform

18. 問題描述 72 32 24 30
300 lb
400 lb 6

19. ANSYS Procedure (1/4) 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17
FINISH
/CLEAR
/TITLE, Lift Platform (lb-in-s)
  B     = 1 ! Width for all members
  E     = 30E6 ! Steel
  NU    = 0.3 ! Steel
/PREP7
  ET, 1, BEAM3
  MP, EX, 1, E
  MP, NUXY, 1, NU
  R, 1, B*8, B*8**3/12, 8 ! Arms
  R, 2, B*4, B*4**3/12, 4 ! Platform
  R, 3, B*2, B*2**3/12, 2 ! Connector
  R, 4, B*2, B*2**3/12, 2 ! Actuator

20. ANSYS Procedure (2/4) 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
  N, 101,   0,  0
  N, 102,   0, 24
  N, 103,  32, 24
  N, 104,  32, 48
  N, 105,  72, 54
  N, 106,  72, 78
  N, 201,  72, 54
  N, 202,  72, 78
  N, 203, 102, 54
  N, 204, 102, 78
  N, 205, 132, 54
  N, 206, 132, 78
  N, 301,  32, 24
  N, 302,  32, 48
  N, 401,  32, 24
  N, 402,  62, -6 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52
  REAL, 1
  E, 101, 103
  E, 103, 105
  E, 102, 104
  E, 104, 106
  REAL, 2
  E, 201, 203
  E, 203, 205
  E, 202, 204
  E, 204, 206
  E, 201, 202
  E, 203, 204
  E, 205, 206
  REAL, 3
  E, 301, 302
  REAL, 4
  E, 401, 402

21. ANSYS Procedure (3/4) 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72
  CP, 1, UX, 105, 201
  CP, 2, UY, 105, 201
  CP, 3, UX, 106, 202
  CP, 4, UY, 106, 202
  CP, 5, UX, 103, 301, 401
  CP, 6, UY, 103, 301, 401
  CP, 7, UX, 104, 302
  CP, 8, UY, 104, 302
  D, 101, UX, 0
  D, 101, UY, 0
  D, 102, UX, 0
  D, 102, UY, 0
  D, 402, UX, 0
  D, 402, UY, 0
  F, 202, FY, -300
  F, 204, FY, -400
  F, 206, FY, -300 74 75 76 77 78 79 80 81 82
  /PNUM, NODE, ON
  EPLOT
  /PNUM, DEFAULT
  FINISH
/SOLU
  SOLVE

22. 11.4.2 ANSYS Procedure (4/4) 84 85 86 87 88 89 /POST1 PLDISP, 2
  ETABLE, MFORX, SMISC, 1
  ETABLE, MFORY, SMISC, 2
  ETABLE, MMOMZ, SMISC, 6

23. 樑元素瀏覽 Overview of Beam Elements
第11.5節
樑元素瀏覽
Overview of Beam Elements

24. Elastic Beams

25. Plastic Beams

26. Finite Strain Beams

27. Unsymmetric Beams

28. Elastic Pipes

29. Plastic Pipes

30. Explicit Dynamics

31. 第11.6節
練習題
Exercises